Nonlinear and dual-parameter chaotic vibrations of lumped parameter model in blisk under combined aerodynamic force and varying rotating speed

In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for blisk structure with lumped parameter model under combined aerodynamic force varying rotating speed. The speed are, respectively, simplified to parametric external excitations. governing equations of motion established by using Hamilton’s principle. free vibration mode localization phenomena studied tuning mistuning blisks. Due mistuning, periodic characteristics destroyed uniform distribution energy is broken. It found that there a positive correlation between variable factor exhibit large in certain region. method multiple scales applied derive four-dimensional averaged 1:1 internal principal resonances. amplitude–frequency response curves studied, which illustrate influence different parameters on bandwidth amplitudes blisk. Lyapunov exponent, bifurcation diagrams, phase portraits, waveforms Poincare maps depicted. exponents diagrams reveal paths leading chaos. influences analyzed. numerical results demonstrate excitations, damping determine occurrence